Nonlinear Transformations for Simplifying Optimization Problems

A new implementation of a symbolic simplification algorithm is presented together with extended theoretical results that support the underlying method for constrained nonlinear optimization problems. The program is capable to automatically recognize simplification transformations, and to detect implicit redundancy in the objective function or in the constraint functions. We have also discussed possibilities to improve the lower and upper bounds obtained by interval arithmetic based inclusion functions. We report computational test results obtained for standard global optimization test problems, and for several other test instances, involving artificially constructed difficult to simplify cases. We also compare the new implementation with a Maple based one reported earlier.